where, in our case where the variables are Gaussian with equal mean vectors, the Hellinger affinity writes (see e.g. [1]}),
\(A(P_{0}^{obs},P_{1}^{obs})=\frac{\det ( G_{0}G_{1})^{1/4}}{\det ((G_{0}+ G_{1})/2)^{1/2}}.\) 
